Integrability Conditions for Lotka-Volterra Planar Complex Quartic Systems Having Homogeneous Nonlinearities

被引：24

作者：

Fercec, Brigita ^{[1
]}

Gine, Jaume ^{[2
]}

Liu, Yirong ^{[3
]}

Romanovski, Valery G. ^{[1
,4
]}

机构：

[1] Univ Maribor, Ctr Appl Math & Theoret Phys, Maribor 2000, Slovenia

[2] Univ Lleida, Dept Matemat, Lleida 25001, Spain

[3] Cent S Univ, Sch Math, Changsha 410083, Hunan, Peoples R China

[4] Univ Maribor, Fac Nat Sci & Math, Maribor 2000, Slovenia

来源：

ACTA APPLICANDAE MATHEMATICAE | 2013年 / 124卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Integrability; Linearizability; Polynomial vector field; Polynomial differential system; ISOCHRONOUS CENTERS; LIMIT-CYCLES; LINEARIZABILITY; POLYNOMIALS; C-2;

D O I：

10.1007/s10440-012-9772-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the integrability problem for the two-dimensional Lotka-Volterra complex quartic systems which are linear systems perturbed by fourth degree homogeneous polynomials, that is, we consider systems of the form , . Conditions for the integrability of this system are found. From them the center conditions for corresponding real system can be derived. The study relays on making use of algorithms of computational algebra based on the Groebner basis theory. To simplify laborious manipulations with polynomial modular arithmetics is involved.

引用

页码：107 / 122

页数：16

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